Abstract:
It is proved that a finally compact $p$-space $X$ is metrizable if and only if the space $X^2\setminus \Delta$ has a countable rectangular open cover. A similar theorem is valid for separable $M$-spaces.
Key words:metrizability, paracompactness, paracompactness off of the diagonal, normality, normality off of the diagonal, final compactness, $p$-space, $M$-space, rectangular covers, Vietoris topology, first axiom of countability.
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